CAREER: Direct Determination of Two-electron Reduced Density Matrices for Many-electron Atoms and Molecules

芝加哥大学的David Mazziotti得到了理论和计算化学研究计划的支持，该计划旨在开发和实施量子力学方法来计算原子和分子的电子结构。这项工作的目的是在没有波函数的情况下直接确定2电子约化密度矩阵(2-RDM)。这种方法的应用包括燃烧和大气化学中的自由基反应，平衡和非平衡分子几何结构下发生的化学现象，以及各种强关联现象。该研究旨在通过两种方法直接计算2-RDM：1)压缩薛定谔方程的解；2)N-可表示条件约束下2-RDM能量的变分最小化。PI和他的团队的最新进展表明，他们的方法可以恢复96-100%的关联能量。一阶半定编程算法将浮点运算和内存中的计算效率提高了许多个数量级。国际数学联合会正在继续并推广一份新的年度出版物，鼓励中学生在数学科学领域追求职业和研究。他正在开发一个研究生班，利用简化密度矩阵的一般概念，将从电子结构到量子信息的化学、物理和数学领域统一起来。这项工作对我们以有用的精度执行多粒子系统的量子计算的能力产生了更广泛的影响，但没有波函数，并鼓励学生培养对数学科学的兴趣。

David Mazziotti of The University of Chicago is supported by the Theoretical and Computational Chemistry program for research to develop and implement quantum mechanical methods to compute the electronic structure of atoms and molecules. The goal of this work is the direct determination of the 2-electron reduced density matrix (2-RDM) without the wave function. Applications of this method include radical reactions in combustion and atmospheric chemistry, chemical phenomena occurring at equilibrium and non-equilibrium molecular geometries, and various strong correlation phenomena. The research aims to calculate the 2-RDM directly via two approaches: 1) Solution of the contracted Schrodinger equation; 2) Variational minimization of the energy with a 2-RDM constrained by N-representability conditions. Recent advances by the PI and his group show that their method can recover 96-100% of the correlation energy. A first-order semidefinite programming algorithm increases the efficiency of the calculations in both floating-point operations and memory by many orders of magnitude. The PI is continuing and extending a new annual publication that encourages secondary students to pursue careers and research in the mathematical sciences. He is developing a graduate class that uses the general concept of reduced density matrices to unite areas of chemistry, physics and mathematics from electronic structure to quantum information. This work is having a broader impact on our ability to perform quantum computations for many-particle systems with useful accuracy but without a wave function, and in encouraging students to foster interests in the mathematical sciences.